In a wireless communication system, a mobile station first needs to perform a random access for establishing communication with a base station. The random access typically includes two steps: (1) Ranging and (2) Resource Request and Allocation. During Ranging, the mobile station sends a signal to the base station, so that the base station can identify the mobile station and measure the power and time delay of the mobile station, and inform the mobile station for power adjustment and time advance. During Resource Request and Allocation, the uplink and downlink resources for communication are requested and allocated. Ranging is a critical part of multi-carrier wireless communication system, and there are several important issues related to ranging:                1. The bandwidth efficiency of the ranging signals        2. The interference of ranging signal with other uplink signals        3. The detection performance and complexity at the base station receiver        
The ranging process typically involves an exchange of messages between the base station and the mobile station by which the mobile station aligns itself with the start of each time slot after compensating for propagation delay and other factors. One problem in a shared medium communication network involves the ranging of many mobile stations. When many mobile stations attempt to perform the ranging simultaneously, they are forced to contend for access to the shared channel and it becomes difficult for any of the mobile stations to complete the ranging process due to the large number of collisions. As a result, the time needed for all of the mobile stations to complete the ranging process is excessive, and much bandwidth on the shared channel is wasted.